GaN has direct bandgap of 3.4eV meaning it can emit 365nm light which is UV. In commercial LEDs they coat GaN in phosphors which when UV light shines on them emits white light. The bandgap of GaN can actually be tuned as well by introducing InGaN which shrinks the bandgap allowing light to be emitted along the visible spectrum.
Prior to using GaN for LEDs, materials used to produce blue LEDs included SiC. Green LEDs (with wavelengths > 555 nm) used GaP:N. Yellow used GaAs(.15)P(.85):N and red used GaAs(.6)P(.4). "Super bright" red LEDs used GaAlAs. This information is from the 1993 Illuminating Engineering Society's Lighting Handbook.
Adding to the respected colleagues, the most important properties of LED materials is that they must have direct bandgap to favor direct band band radiative recombination rather than nonradiative recombination via traps according to SHockley Read Hall recombination mechanism. So, also the radiative recombination lifetime must be much smaller than the nonradiative lifetime to increase the electrical to light conversion efficiency. This requires that the material is fabricated as a single crystal material with very low chemical and geometrical defects that can act as effective recombination centers. This is very important issue for the material properties.